تقدير أنموذج انحدار لوجستي لمتغير معتمد متعدد المستويات مع تطبيق عملي

Estimating a logistic Model for a Multi-level Dependent Variable with Practical Application

ABSTRACT :
Statistics form an extended hand that provides its services over time to other sciences and a tributary that contributes to analyzing the results of studies in various fields. The experiment and the identification of the factors affecting the course of the experiment, its development and access to the required results. In this thesis, nonlinear regression was used and a focus on the regression of the logistic curve.
The problem of the thesis lies in how to deal with the multi-level logistic regression model in the data modeling process and to reach the optimal estimation methods in estimating parameters
The thesis aims to estimate the logistic regression model for a dependent variable (multi-levels) (Yijk), depending on descriptive variables to know the extent of their impact on the dependent variable (under study), where the classical estimation methods were used, including (the method of greatest possibility [MLE] and the method of least squares). weighted [WLS]) and intelligent (the method of artificial neural networks [ANN] and genetic algorithm [GA]), and then compare between the methods to find out the best and most efficient of them in order to obtain the efficient capabilities to rely on in standing on the dimensions and variables of the phenomenon (under study Through the use of comparison scales, including mean squared error (MSE) and mean absolute error (MAE).
In practice, and to achieve the objectives of the thesis, a simulation experiment was conducted using the Monte Carlo method for different sample sizes (small, medium, large) with sizes (25, 75, 125) that fit the experience of practical application to reach the optimal method and to know the changes that occur in The process of experimentation, and then the results of the simulation experiment were summarized, and from the course of the simulation experiment, it was concluded that the method of artificial neural networks is the best among the methods used in the estimation process. In the estimation process on the applied side as well, and not only in the experimental side, in order to match the estimation methods, where the results of the applied side showed the superiority of the method of artificial neural networks also among the Its peers, and this is consistent with the experimental side, which indicates the suitability of the estimation method with the logistic regression model.
Finally, one of the most important conclusions that the connection is superior to the method of artificial neural networks (ANN) in the experimental and applied aspect to the rest of the methods used, the thesis also showed the possibility of converting the logistic model from the non-linear model to the linear model.